Piezoelectric resonator element, piezoelectric resonator, and acceleration sensor

ABSTRACT

A piezoelectric resonator element includes: a resonating arm extending in a first direction and cantilever-supported; a base portion cantilever-supporting the resonating arm; and an excitation electrode allowing the resonating arm to perform flexural vibration in a second direction that is orthogonal to the first direction. In the piezoelectric resonator element, the resonating arm includes an adjusting part adjusting rigidity with respect to a bend in a third direction that is orthogonal to the first and second directions.

BACKGROUND

1. Technical Field

The present invention relates to a piezoelectric resonator element, apiezoelectric resonator, and an acceleration sensor that reducesensitivity in other axis.

2. Related Art

In tuning fork type quartz crystal resonators, shapes of front and backfaces (XY plane) of a resonating arm are commonly symmetrical. JP-A2004-200917, for example, discloses a tuning fork type quartz crystalresonator including a resonating arm that has a recessed groove on itsfront and back faces. Tuning fork type quartz crystal resonators can beused as an acceleration sensor for detecting acceleration in Y-axisdirection when a longitudinal direction of a resonating arm thereof isdefined as Y-axis. In a case where the tuning fork type quartz crystalresonators perform accelerated motion toward +Z-axis direction that is athickness direction of the resonators the resonating arm of theresonators is affected by inertia force so as to bend in −Z-axisdirection. On the other hand, in a case where the tuning fork typequartz crystal resonators perform accelerated motion toward −Z-axisdirection, the resonating arm thereof bends in +Z-axis direction.

The inventor surveyed distribution of stress in a state that aresonating arm of a tuning fork type piezoelectric resonator composed ofa Z-cut quartz crystal plate is bent, and found that the stressconcentrates on a plane at +Z plane side. That is, the inventor foundthat a neutral plane that receives no compression and no tension byflexure is disproportionately formed at the +Z plane side. Accordingly,the rigidity at the +Z plane side of the tuning fork type quartz crystalresonator is higher than that at −Z plane side.

The tuning fork type quartz crystal resonator is mainly composed of theZ-cut quartz crystal plate as described above. In this case, the bondingstate of crystal in the thickness direction is asymmetric, whereby theresonator has anisotropy in the thickness direction. That is, in a casewhere the tuning fork type quartz crystal resonator is turned over, analignment of crystal of the resonator is not same as that before theturning over of the resonator. It is considerable that an elasticconstant, a piezoelectric constant, and the like that relate to bendingstress on the +Z plane are not same as those on the −Z plane due to theanisotropy so as to generate difference of rigidity, whereby therigidity at the +Z plane side is higher in a case of quartz crystal.

In a case where the tuning fork type quartz crystal resonator in whichthe rigidity at the +Z plane side is different from that at the −Z planeside is used as an acceleration sensor for detecting acceleration inY-axis direction, the acceleration sensor responds to acceleration inZ-axis direction, that is, the sensitivity in other axis is generated.Therefore, an accurate detecting result of acceleration in Y-axisdirection can not be obtained.

It is considerable that such problem of the sensitivity in other axisoccurs as follows. In a case where the rigidity at the +Z plane sidewith respect to flexure in Z-axis direction and that at the −Z planeside are unbalanced, if the tuning fork type quartz crystal resonator isexcited so as to be allowed to perform flexural vibration, the +Z planeside from the neutral plane described above has strong rigidity withrespect to the flexural vibration and the −Z plane side has weakrigidity. As a result, amplitude of vibration at the −Z plane sidebecomes larger than that at the +Z plane side. Therefore, the resonatingarm is drawn toward the +Z plane side due to tensile stress from the +Zplane that has large rigidity at a part where the amplitude of vibrationis large. Accordingly, the resonating arm does not vibrate horizontallyto a plane formed by the tuning fork type quartz crystal resonatorhaving a plate shape as a whole. That is, the resonating arm of thetuning fork type quartz crystal resonator vibrates not only in X-axisdirection but also in Z-axis direction. In a case where the tuning forktype quartz crystal resonator performs accelerated motion under suchvibrating state, a vibrating component in Z-axis direction of theresonating arm receives inertia force due to the acceleration in Z-axisdirection, whereby a vibrating frequency in Z-axis direction varies. Inaccordance with the variation of the vibrating frequency in Z-axisdirection, the resonance frequency of the resonating arm vibrating inX-axis direction varies. Then, this effect appears as a noise togetherwith a desired resonance frequency of the tuning fork type quartzcrystal resonator.

SUMMARY

An advantage of the present invention is to provide a piezoelectricresonator element in which the rigidities of both faces thereof withrespect to the flexural vibration described above are balanced andsensitivity in other axis is reduced; a piezoelectric resonator providedwith the piezoelectric resonator element; and an acceleration sensorprovided with the same.

The above advantage can be attained by the following aspects of theinvention.

A piezoelectric resonator element according to a first aspect of theinvention includes: a resonating arm extending in a first direction andcantilever-supported; a base portion cantilever-supporting theresonating arm; and an excitation electrode exciting the resonating armto perform flexural vibration in a second direction that is orthogonalto the first direction. In the resonator element, the resonating armincludes an adjusting part for the rigidity with respect to a bend in athird direction that is orthogonal to the first direction and the seconddirection.

In the piezoelectric resonator element composed of a piezoelectricplate, rigidities with respect to a bending stress and the like on facesare sometimes different from each other due to the anisotropy of theplate. If such piezoelectric resonator element is excited to performflexural vibration by the excitation electrode, the vibration includesnot only a component in a predetermined vibrating direction but also acomponent of vibration in a direction that is orthogonal to thepredetermined vibrating direction. Therefore, according to the firstaspect, striking the balance between the rigidities with respect to theflexural vibration can reduce a component of vibration in a directionthat is orthogonal to the direction of the flexural vibration of theresonating arm. Accordingly, the piezoelectric resonator element thatreduces the occurrence of deviation, which is caused by the accelerationfrom the third direction, of the resonance frequency of the flexuralvibration can be formed,

A piezoelectric resonator element according to a second aspect of theinvention includes: a resonating arm composed of a Z-cut piezoelectricplate and cantilever-supported in a longitudinal direction; a baseportion cantilever-supporting the resonating arm; and an excitationelectrode exciting the resonating arm to perform flexural vibration in adirection orthogonal to a thickness direction. In the resonator element,the resonating arm includes an adjusting part adjusting rigidity withrespect to a bend in the thickness direction.

The piezoelectric resonator element composed of the Z-cut piezoelectricplate has different rigidities with respect to the bending stress andthe like on the +Z plane and on the −Z plane due to its anisotropy. Ifsuch piezoelectric resonator element is excited to perform a flexuralvibration by the excitation electrode, the vibration includes not only acomponent of vibration horizontal to a plane formed by the piezoelectricresonator element having a plate shape but also a component of vibrationin an orthogonal direction (thickness direction) to the plane.Therefore, according to the second aspect, striking the balance betweenthe rigidities with respect to the flexural vibration can reduce thecomponent of vibration in the thickness direction of the resonatingarms. Accordingly, the piezoelectric resonator element that reducesoccurrence of deviation, which is caused by the acceleration from thethickness direction, of the resonance frequency of the flexuralvibration can be formed.

In the piezoelectric resonator element of the second aspect, theadjusting part may be a groove formed from a base portion side of a +Zplane of the resonating arm along a free end side direction of theresonating arm.

In the resonator element of the aspect, the groove is formed on the +Zplane of the resonating arm in a manner positioned at the base portionside, which is a portion receiving the strongest bending stress due tothe flexural vibration of the piezoelectric resonator element, so thatthe rigidity with respect to the bending stress caused by the flexuralvibration at the +Z plane side is effectively reduced, striking thebalance between the rigidity at the +Z plane side and that at the −Zplane side of the resonating arm. Consequently, the component of theflexural vibration in the thickness direction of the resonating arm canbe reduced. Accordingly, the piezoelectric resonator element in whichthe detecting sensitivity of the acceleration in the thicknessdirections that is, the sensitivity in other axis is reduced can beformed.

In the piezoelectric resonator element of the second aspect, theadjusting part may be a recess formed at the base portion side of the +Zplane of the resonating arm.

In the resonator element of the aspect, the recess is formed on the +Zplane of the resonating arm in a manner positioned at the base portionsides which is a portion receiving the strongest bending stress due tothe flexural vibration of the piezoelectric resonator element, so thatthe rigidity with respect to the bending stress caused by the flexuralvibration at the +Z plane side can be effectively reduced only byetching a smaller region than the case of the groove described above.Further, a high-accurate patterning such that positioning of the grooveis conducted by photolithography is not required, being able to increasea yield in manufacturing a piezoelectric resonator element.

In the piezoelectric resonator element of the second aspect, theadjusting part may include a first groove formed from the base portionside of the +Z plane of the resonating arm along the free end directionof the resonating arm and a second groove formed from the base portionside of a −Z plane of the resonating arm along the free end direction ofthe resonating arm, and the first groove may be formed deeper than thesecond groove.

In the resonator element of the aspect, the grooves are formed on bothfaces of the resonating arm in a manner positioned at the base portionside, which is a portion receiving the strongest bending stress due tothe flexural vibration of the piezoelectric resonator element, beingable to decrease a CI value of the piezoelectric resonator element.Further, forming the groove on the +Z plane side deeper than that on the−Z plane reduces a relative intensity difference between the rigiditywith respect to the bending stress caused by the flexural vibration atthe +Z plane side and the rigidity at the −Z plane side so as to strikethe balance between the rigidities with respect to the flexuralvibration of the resonating arm at the +Z plane side and at the −Z planeside, being able to reduce the component of the flexural vibration inthe thickness direction of the resonating arm. Accordingly, thepiezoelectric resonator element in which the detecting sensitivity ofacceleration in the thickness direction, that is, the sensitivity inother axis is reduced and have a low CI value can be formed.

In the piezoelectric resonator element of the second aspect, theadjusting part may include a first groove formed from the base portionside of the +Z plane of the resonating arm along the free end directionof the resonating arm and a second groove formed from the base portionside of the −Z plane of the resonating arm along the free end directionof the resonating arm, and an end at the base portion side of the firstgroove may be positioned closer to the base portion than an end at thebase portion side of the second groove.

In the resonator element of the aspect, the groove is formed on the +Zplane side of the resonating arm in a manner positioned at the baseportion side, which is a portion receiving the strongest bending stressdue to the flexural vibration of the piezoelectric resonator element, sothat the rigidity with respect to the bending stress caused by theflexural vibration at the +Z plane side is effectively reduced, beingable to strike the balance between the rigidity at the +Z plane side andthat at the −Z plane side. Further, the groove at the +Z plane and thegroove at the −Z plane do not interfere with each other in the depthdirection. Therefore, the design versatility in the depth direction ofthe groove is further improved. At the same time, since the groove canbe designed deeper, the piezoelectric resonator element that has afurther reduced CI value can be formed. Further, since asymmetryproperty in the thickness direction is further improved, suppressingeffect of an occurrence of unnecessary vibration caused by the thicknessdimension can be improved.

The piezoelectric resonator element of the second aspect, an overlappingregion in which the end at the base portion side of the second groove ispositioned closer to the base portion than the end at a free end side ofthe first groove and the first groove and the second groove areoverlapped with each other when they are viewed from the thicknessdirection may be formed at the end at the base portion side of thesecond groove.

In such structure, the groove at the +Z plane side and the groove at the−Z plane side do not interfere with each other in the depth direction,improving the design versatility of the grooves in the depth direction.Further, the resonating arm is thin in the thickness direction and thedistance between the excitation electrodes formed in the grooves of theboth faces is short in the overlapping region, being able to apply largeelectrical field to the overlapping region. Therefore, the piezoelectricresonator element having further reduced CI value can be formed, Inaddition, a groove region contacts with an etchant more sparsely than anouter shape region, so that the etching velocity in the groove region isslower than that in the outer shape region. Therefore, no particularprocess for digging the groove is required and the groove can be formedat the same time with the outer shape blanking of the piezoelectricresonator element, being able to form the piezoelectric resonatorelement having a higher yield.

In the piezoelectric resonator element of the second aspect, theadjusting part may include a first groove formed from the base portionside of the +Z plane of the resonating arm along the free end directionof the resonating arm, a second groove formed from the base portion sideof the −Z plane of the resonating arm along the free end direction ofthe resonating arm, and a beam formed at the base portion side of thesecond groove.

In such structure, the groove can be formed short so as to make the baseportion side, which is a portion receiving the strongest bending stressdue to the flexural vibration of the piezoelectric resonator element, ofthe resonating arm thick. Therefore, even though the beam is formedshort, the rigidity with respect to the bending stress caused by theflexural vibration at the −Z plane side is increased relatively to thatat the +Z plane side so as to strike the balance between the rigidity atthe +Z plane side and that at the −Z plane side. Further, since thelength of the groove to which the excitation electrode film is formedcan be sufficiently secured, an electrode of the piezoelectric resonatorelement can be widely formed in the groove. Since the grooves are formedon the both faces, the piezoelectric resonator element having an ICvalue that is not inferior to that of the above piezoelectric resonatorelement can be formed. Further, forming the beam improves the asymmetryproperty in the thickness direction, improving the suppressing effect ofthe occurrence of the unnecessary vibration depending on the thicknessdimension.

In the piezoelectric resonator element of the second aspect, the beammay be formed apart from the base portion side to the free end side ofthe second groove.

In such structure, as the beam is moved to be farther from the baseportion side and closer to the free end side in the groove on the −Zplane, the rigidity with respect to the bending stress caused by theflexural vibration on the −Z plane can be decreased. Therefore, properdetermination of the position of the beam can fine adjust the rigidityat the −Z plane of the resonating arm. In addition, if the position ofthe beam is properly determined, the degree of the asymmetry in thethickness direction can be determined, being able to optimize forsuppressing the unnecessary vibration.

In the piezoelectric resonator element of the first aspect, theadjusting part may include a first electrode film formed on the +Z planeof the resonating arm and a second electrode film formed on the −Z planeof the resonating arm and being thinner than the first electrode film.

In such structure, the electrode film on the −Z plane is formed thickerthan that on the +Z plane without conducting a specific etchingtreatment for forming the groove and the like described above on thepiezoelectric resonator element so as to relatively increase therigidity with respect to the bending stress caused by the flexuralvibration at the −Z plane side. Thus, the rigidities with respect to theflexural vibration of the both faces are balanced so as to be able toreduce a component of the flexural vibration in the thickness directionof the resonating arm. Accordingly, the piezoelectric resonator elementin which the detecting sensitivity of the acceleration in the thicknessdirection, that is, the sensitivity in other axis is reduced can beformed. Further, since the piezoelectric resonator element requires nogrooves, for example, formed thereon, a manufacturing process does notbecome complex, being able to increase a yield of manufacturing thepiezoelectric resonator element. Further, if this structure is appliedto the piezoelectric resonator element having any of the structuresdescribed above, the balance of the rigidities with respect to theflexural vibration is adjusted not only by the grooves and the like butalso by the electrode films. Therefore, the adjusting range of therigidities of the resonating arm is expanded, being able to moreeffectively reduce the sensitivity in other axis.

In the piezoelectric resonator element of the first aspect, theresonating arm may include two resonating arms, the excitation electrodemay include a plurality of excitation electrodes, the two resonatingarms may be cantilever-supported at the base portion in parallel, and anexcitation electrode formed on one resonating arm and another excitationelectrode formed on the other resonating arm may be coupled by crosswiring

In such structure, the two resonating arms are formed in parallel fromthe base portion in a cantilever-supported state so as to be formed in atuning fork type. Further, the excitation electrodes are cross-wired tothe resonating arms. Accordingly, the tuning fork type piezoelectricresonator element that can perform an opposite phase vibration, that is,the flexural vibration in which the resonating arms move close to andapart from each other, as the fundamental wave mode, can be formed.Further, if any of the structures described above is applied to thepiezoelectric resonator element, a piezoelectric resonator element inwhich the acceleration in the thickness direction, that is, thesensitivity in other axis is reduced can be formed.

A piezoelectric resonator and an acceleration sensor according to thirdand fourth aspects include the piezoelectric resonator element of any ofthe first and second aspects. The piezoelectric resonator element ismounted in a cantilever-supported state in which the base portion of theresonator element is used as a fixed end.

According to the third aspect, the piezoelectric resonator including thepiezoelectric resonator element that uses the first direction or thelongitudinal direction as a detecting axis and reduces the sensitivityin other axis by reducing a component of vibration in the Z-axisdirection of the flexural vibration can be formed. According to thefourth aspect, the acceleration sensor including the piezoelectricresonator element that uses the first direction or the longitudinaldirection as the acceleration detecting axis and reduces the sensitivityin other axis by reducing a component of vibration in the Z-axisdirection of the flexural vibration can be formed. Further, thefrequency adjustment after the mounting is conducted at the free endside of the resonating arm, while the rigidity adjustment is conductedat the base portion side of the resonating arm. Therefore, the frequencyadjustment and the rigidity adjustment do not interfere to each other soas to be conducted independently.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described with reference to the accompanyingdrawings, wherein like numbers reference like elements.

FIGS. 1A to 1C are schematic views showing a tuning fork typepiezoelectric resonator element according to a first embodiment.

FIGS. 2A and 2B are A-A line sectional views showing a neutral face in acase where the tuning fork type piezoelectric resonator element bends ina thickness direction.

FIGS. 3A and 3B are schematic views showing a tuning fork typepiezoelectric resonator element according to a second embodiment.

FIG. 4 is an A-A line sectional view showing a tuning fork typepiezoelectric resonator element according to a third embodiment.

FIGS. 5A to 5C are schematic views showing a tuning fork typepiezoelectric resonator element according to a fourth embodiment.

FIGS. 6A and 6B are B-B line sectional views showing a tuning fork typepiezoelectric resonator element according to a fifth embodiment.

FIGS. 7A and 7B are B-B line sectional views showing a tuning fork typepiezoelectric resonator element according to a sixth embodiment.

FIG. 8 is a schematic view showing an acceleration sensor according to aseventh embodiment.

FIGS. 9A to 9D are schematic views showing stress distribution in a casewhere a tuning fork type piezoelectric resonator element bends in thethickness direction.

FIGS. 10A and 10B are tables showing a result of a simulation offrequency variation of the tuning fork type piezoelectric resonatorelement.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Embodiments of a piezoelectric resonator element, a piezoelectricresonator, and an acceleration sensor according to the present inventionwill be described below based on a tuning fork type piezoelectricresonator element with reference to the accompanying drawings. It shouldbe noted that the embodiments are applicable to a piezoelectricresonator element having one resonating arm or a piezoelectric resonatorelement having two or more of resonating arms.

First Embodiment

FIGS. 1A to 1C schematically show a tuning fork type piezoelectricresonator element according to a first embodiment of the invention. FIG.1A is an overall view, and FIGS. 1B and 1C are sectional views takenalong the A-A line of FIG. 1A. Note that later-described embodimentshave a whole outer shape that is same as that of the first embodiment,so that the A-A line and the B-B line in FIG. 1A are applied to otherembodiments. Further, note that directions of X axis, Y axis, and Z axisthat are orthogonal to each other in FIGS. 1A to 1C and a relationbetween the axes and the tuning fork type piezoelectric resonatorelement are applied to other embodiments. Furthermore, note thatflexural vibration of the tuning fork type piezoelectric resonatorelement is a fundamental wave mode in each of the embodiments.

The piezoelectric resonator element according to the first embodiment iscomposed of a Z-cut piezoelectric plate and includes two resonating armscantilever-supported in a longitudinal direction; a base portioncantilever-supporting the resonating arms; and excitation electrodesallowing the resonating arms to perform flexural vibration in anorthogonal direction to the thickness direction. The two resonating armsare formed in parallel on the base portion to be cantilevered. Theexcitation electrode formed on one resonating arm is coupled with theexcitation electrode formed on the other resonating arm by cross wiring.The resonating arms include an adjusting part for rigidity with respectto a bend in the thickness direction. The adjusting part is a grooveformed on a +Z plane from a base portion side of the arms along a freeend direction of the arms.

FIG. 1A is a plan view showing a tuning fork type piezoelectricresonator element 10 according to the first embodiment. The bottom viewof the tuning fork type piezoelectric resonator element 10 is symmetricto the plan view of the same. The difference is that the bottom viewdoes not have a groove 26. The tuning fork type piezoelectric resonatorelement 10 is made of a piezoelectric material such as quartz crystal,lithium tantalite, and lithium niobate. In a case of quartz crystal, a Zplane of which a normal line direction is Z axis that is one of quartzcrystal axes is used. The crystal is practically cut such that thenormal line of the Z plane forms a deflection angle of about 10 degreesat most with respect to the Z axis. The tuning fork type piezoelectricresonator element 10 includes a base portion 12 and a pair of resonatingarms 14 extending from the base portion 12.

FIG. 1B is an enlarged sectional view showing the A-A line section ofthe tuning fork type piezoelectric resonator element 10 (the excitationelectrodes are omitted for the description) shown in FIG. 1A. FIG. 1C isan enlarged sectional view showing the A-A line section of the tuningfork type piezoelectric resonator element 10 (with the excitationelectrodes) shown in FIG. 1A. The resonating arms 14 have a +Z plane 16(front face in a broad sense), and a −Z plane 18 (back face in a broadsense) that face opposite directions with each other, and a firstlateral face 20 and a second lateral face 22 connecting the +Z plane 16and the −Z plane 18 at the both sides.

On the other hand, the resonating arms 14 are cantilever-supported onthe base portion 12 in such manner that the first lateral face 20 of oneresonating arm 14 (left side in FIG. 1B) and the second lateral face 22of the other resonating arm 14 (right side in FIG. 1B) are arranged inparallel to face each other. Therefore, an end, at the base portion 12side, of the resonating arms 14 of the tuning fork type piezoelectricresonator element 10 is a fixed end, while the other end is a free end.In a case where the resonating arms 14 are allowed to perform theflexural vibration as the fundamental wave mode, the end at the baseportion 12 side of the resonating arms 14 is a part that receives thestrongest bending stress caused by the flexural vibration and the end atthe free end side is a part that vibrates in the largest amplitude.

The resonating arm 14 has a root portion 24 (fixed end) connected to thebase portion 12 and widened toward the base portion 12 side. Thus theresonating arm 14 is connected to the base portion 12 in its large-widthportion, having high rigidity.

Each of the resonating arms 14 has the groove 26 formed on the +Z plane16 and extending in the longitudinal direction. The groove 26 has alength equal to 50% to 70% of that of the resonating arms 14 in thelongitudinal direction. The groove 26 has a width equal to 60% to 90% ofthat of the resonating arms 14. The groove 26 includes a first innerface 28 extending back on to the first lateral face 20, and a secondinner face 30 extending back on to the second lateral face 22.

The groove 26 can decrease the rigidity with respect to the flexuralvibration of the resonating arm 14 and at the same time, can form strongelectrical fields between the first lateral face 20 and the first innerface 28 and between the second lateral face 22 and the second inner face30, being able to obtain a high inverse piezoelectric effect. As aresult, the resonating arms 14 can be effectively vibrated so as to beable to decrease a crystal impedance (CI) value. If the groove 26 isformed on the +Z plane 16 and on the other hand, no groove is formed onthe −Z plane or a shallow or small groove is formed on the −Z plane, asdescribed later, the difference between the rigidity with respect to theflexural vibration at the +Z plane 16 side and that at the −Z plane sidecan be cancelled.

The base portion 12 has a pair of constricted portions 32 opposed toeach other so as to narrow the width thereof in the width direction(X-axis direction). The pair of constricted portions 32 is formedbetween mount parts 34 and the resonating arms 14 of the tuning forktype piezoelectric resonator element 10. Therefore, the constrictedportions 32 block the transmission of vibration of the resonating arms14 to suppress the transmission of the vibration (vibration leakage)through the base portion 12 and the resonating arms 14 to the outside,being able to prevent an increase of the CI value. As the length (depth)of the constricted portions 32 is made longer (deeper) to the extentthat the strength of the base portion 12 can be secured, the suppressingeffect of the vibration leakage is increased,

As shown in FIG. 1C, excitation electrode films are formed on theresonating arms 14. The excitation electrode films may have a multilayerstructure including a Cr film serving as an underlying film having athickness from 100 Å or more to 300 Å or less and an Au film having athickness from 200 Å or more to 500 Å or less formed on the Cr film. TheCr film has high adhesion to quartz crystal and the Au film has lowelectric resistance and is resistant to oxidizing. The excitationelectrode films include a first lateral face electrode 36 formed on thesecond lateral face 22; a second lateral face electrode film 38 formedon the first lateral face 20; a first inner face electrode film 40formed on the second inner face 30; a second lateral face electrode film42 formed on the first inner face 28; and a bottom face electrode film44 formed on the −Z plane 18.

The first inner face electrode film 40 and the second inner faceelectrode film 42 are continuously formed in one groove 26 so as to beelectrically connected with each other, forming a first excitationelectrode film 46.

The first lateral face electrode film 36 and the second lateral faceelectrode film 38 formed on one resonating arm 14 so as to beelectrically connected with each other, forming a second excitationelectrode film 48.

The bottom face electrode film 44 forms a third excitation electrodefilm 50.

Here, the two resonating arms 14 are called a first resonating arm 14and a second resonating arm 14. The first excitation electrode film 46formed on the groove 26 of the first resonating arm 14 is coupled to anextraction electrode film 52 formed on the +Z plane 16 of the baseportion 12 so as to be coupled to the second excitation electrode film48 formed on the lateral face of the second resonating arm 14. The thirdexcitation electrode film 50 formed on the −Z plane 18 of the firstresonating arm 14 is coupled to an extraction electrode film (not shown)formed on the −Z plane 18 of the base portion 12 so as to be coupled tothe second excitation electrode film 48 formed on the lateral face ofthe second resonating arm 14. The first lateral face electrode film 36and the second lateral face electrode film 38 formed on the both lateralfaces of the second resonating arm 14 are coupled to each other througha connecting electrode film 54 formed on at least one of the +Z plane 16and the −Z plane 18 of the resonating arm 14 at the end side of the arm.The connecting electrode film 54 is allowed to serve as a weight foradjusting a frequency. For example, a resonating frequency can beincreased by decreasing a mass of the connecting electrode film 54.

In the first embodiment, a voltage is applied between the first lateralface electrode film 36 and the first inner face electrode film 40,between the first lateral face electrode film 36 and the bottom faceelectrode film 44, between the second lateral face electrode film 38 andthe second inner face electrode film 42, and between the second lateralface electrode film 38 and the bottom face electrode film 44. Thus onelateral end of the resonating arm 14 is extended and the other lateralend is contracted so as to bend and vibrate the resonating arm 14. Inother words, a voltage is applied between the first excitation electrodefilm 46 and the second excitation electrode film 48 and between thethird excitation electrode film 50 and the second excitation electrodefilm 48 in one resonating arm 14 so as to expand and contract the firstlateral face 20 and the second lateral face 22 of the resonating arm 14,allowing the resonating arm 14 to perform the flexural vibration. It isfound that as the length of the first and second excitation electrodefilms 46 and 48 in the longitudinal direction is increased, within anextent up to 70% of the length of the resonating arm 14, the CI value isdecreased.

An operation of the tuning fork type piezoelectric resonator element 10according to the first embodiment will be described with reference toFIG. 1C. Referring to FIG. 1C, a voltage is applied between the firstexcitation electrode film 46 and the second excitation electrode film 48and between the third excitation electrode film 50 and the secondexcitation electrode film 48 in the first resonating arm 14, and avoltage is applied between the first excitation electrode film 46 andthe second excitation electrode film 48 and between the third excitationelectrode film 50 and the second excitation electrode film 48 in thesecond resonating arm 14.

Here, the first excitation electrode films 46, the second excitationelectrode films 48, and the third excitation electrode films 50 arecoupled to an alternating-current power supply by cross-wiring. Thecross-wiring is such wiring that the first excitation electrode film 46and the third excitation electrode film 50 of the first resonating arm14 (positioned at the left side) have the same electric potential(+potential in the example in FIG. 1C) as that of the second excitationelectrode film 48 of the second resonating arm 14 (positioned at theright side), while the second excitation electrode film 48 of the firstresonating arm 14 (positioned at the left side) has the same electricalpotential (−potential in the example in FIG. 1C) as that of the firstexcitation electrode film 46 and the third excitation electrode film 50of the second resonating arm 14 (positioned at the right side). Thus analternating voltage serving as a driving voltage is applied to theseelectrode films 46, 48, and 50. Applying the voltage generates electricfields, as shown by arrows in FIG. 1C, so as to excite the resonatingarms 14 such that they vibrate in opposite phases to each other (theyvibrate such that the free ends of the resonating arms 14 move close toand apart from each other within a plane of which the normal line is theZ axis), thus performing flexural vibration. The alternating voltage isadjusted such that the resonating arms 14 vibrate in the fundamentalmode.

FIGS. 2A and 2B are sectional views taken along the A-A line of FIG. 1A.FIGS. 2A and 2B show a state, which is generated in a case where thetuning fork type piezoelectric resonator element 10 is bent in theZ-axis direction, of the neutral plane. FIG. 2A shows a case where thegroove 26 is not formed, while FIG. 2B shows a case where the groove 26is formed. As described above, in a case where an acceleration works inthe Z-axis direction, the tuning fork type piezoelectric resonatorelement 10 bends, so that the tensile stress acts on the +Z plane 16side and the compressive stress acts on the −Z plane 18 side. Theneutral face 56 on which neither compression nor tension is generated isformed closer to the +Z plane 16 in the resonating arms 14, as shown inFIG. 2A. If such tuning fork type piezoelectric resonator element 10 isallowed to perform the flexural vibration, the vibration includes notonly a vibrating component in the X-axis direction but also a vibratingcomponent in the Z-axis direction. As a result, the vibrating componentin the Z-axis direction in the flexural vibration receives inertia forcedue to the acceleration, fluctuating the vibrating frequency of theflexural vibration in the Z-axis direction. Accordingly, the resonancefrequency of the flexural vibration in the X-axis direction of theresonating arms is fluctuated.

On the other hand, if the groove 26 is formed as shown in FIG. 2B, theresonating arms 14 having a one-face recessed section are formed. In theflexural vibration of the tuning fork type piezoelectric resonatorelement 10 in such state, the rigidity at the +Z plane 16 side withrespect to the flexural vibration is effectively reduced because thegroove 26 is formed from the root portion 24, which is a portionreceiving the strongest bending stress due to the flexural vibration andpositioned at the base portion 12 side, to the free end side, so as toremove the portion contributing to the rigidity with respect to theflexural vibration of the resonating arms 14. In this case, the neutralface 56 is shifted to an intermediate part in the thickness direction asshown in FIG. 2B, the difference between a bending moment of a componentat the +Z plane 16 side from the neutral face 56 and a bending moment ofa component at the −Z plane 18 side from the neutral face 56 is reduced,reducing the vibrating component in the Z-axis direction in the flexuralvibration. Therefore, even if the tuning fork type piezoelectricresonator element 10 receives the acceleration from the Z-axisdirection, the inertia force that the flexural vibration receives due tothe acceleration from the Z-axis direction can be controlled to besmall, being able to reduce the detecting sensitivity of theacceleration from the Z-axis direction.

As described above, the piezoelectric resonator element composed of theZ-cut piezoelectric plate has different rigidities with respect to thebending stress and the like on the +Z plane 16 and on the −Z plane 18due to its anisotropy. Such piezoelectric resonator element is allowedto perform the flexural vibration by the excitation electrodes, thevibration includes not only a component of vibration horizontal to aplane formed by the piezoelectric resonator element having a plate shapebut also a vibrating component in an orthogonal direction (thicknessdirection) to the plane. Therefore, according to the first embodiment,striking the balance between the rigidities with respect to the flexuralvibration can reduce the vibrating component in the thickness directionof the resonating arms. Accordingly, the piezoelectric resonator elementthat reduces occurrence of deviation, which is caused by theacceleration from the thickness direction, of the resonance frequency ofthe flexural vibration can be formed. Further, according to the firstembodiment, the groove 26 is formed on the +Z plane 16 of the resonatingarms 14 in a manner positioned at the base portion 12, which is a partreceiving the strongest bending stress due to the flexural vibration ofthe piezoelectric resonator element, so that the rigidity with respectto the bending stress caused by the flexural vibration at the +Z plane16 side is effectively reduced, striking the balance between therigidity at the +Z plane 16 side and that at the −Z plane 18 side of theresonating arms. Accordingly, the component of the flexural vibration inthe thickness direction of the resonating arms 14 can be reduced.Therefore, the piezoelectric resonator element of which the detectingsensitivity of the acceleration in the thickness direction, that is, thesensitivity in other axis is reduced can be formed. The two resonatingarms 14 are formed in parallel to each other from the base portion in acantilever-supported state so as to be formed in a tuning fork type.Further, the excitation electrodes are cross-wired to the resonatingarms 14. Accordingly, the tuning fork type piezoelectric resonatorelement that performs the flexural vibration, in which the resonatingarms 14 move close to and apart from each other, as the fundamental wavemode, that is, a resonator element that can perform an opposite phasevibration can be formed. Further, if any of the following embodimentsdescribed later is applied to the piezoelectric resonator elementdescribed above, a piezoelectric resonator element in which theacceleration in the thickness direction, that is, the sensitivity inother axis is reduced can be formed.

FIG. 9A is a sectional view taken along the C-C line of FIG. 9D thatschematically shows the tuning fork type piezoelectric resonator element10. FIG. 9A shows a state that the resonator element 10 iscantilever-supported on the base portion 12 and an acceleration a isapplied in the Z-axis direction. Here, note that crystal axes of quartzcrystal of the tuning fork type piezoelectric resonator element 10 aresame as those in FIG. 1A, but the constricted portion, the groove, andthe excitation electrodes are omitted so as to simplify the drawing. Theresonating arms made of quartz crystal are set to have a length of 3200μm and a width of 204 μm.

In a case where the acceleration a is applied in the Z-axis direction,that is, the normal line direction of the +Z plane 16, the inertia forceworks in the −Z plane 18 direction that is opposite to the direction inwhich the acceleration a is applied, in the resonating arms 14. As aresult, the resonating arms 14 bend, so that the tensile stress isapplied to the vicinity of the +Z plane 16 of the resonating arms 14 inthe Y-axis direction (longitudinal direction), while the compressivestress is applied at the vicinity of the −Z plane 18 of the resonatingarms 14 in the Y-axis direction.

The inventor simulated stress distribution in the Y-axis direction underthe condition of the acceleration α of 500 G (G denotes an absolutefigure of acceleration due to gravity) in FIG. 9A. FIG. 9B (Y-Z plane)shows a simulation result of the stress distribution in a region 76 thatis at the vicinity of the root portion 24, while the FIG. 9C (X-Z plane)shows a simulation result of the stress distribution (neutral face) onthe D-D line section.

As apparent from FIGS. 9A and 9B, the stress in the Y-axis directioncontinuously varies from a tensile stress to a compressive stress as aposition is apart from the +Z plane 16 to be close to the −Z plane 18 soas to form a face on which the stress in the Y-axis direction becomesnil, that is, the neutral face 56. The inventor found that a distancebetween the neutral face 56 and the +Z plane 16 was shorter than thedistance between the neutral face 56 and the −Z plane 18, that is, theneutral face 56 was shifted, from the simulation. The inventorconsidered that the shift of the neutral face 56 occurred because therigidity with respect to the bending stress caused by the bend in theZ-axis direction at the +Z plane 16 side of the quartz crystal is higherthan the rigidity at the −Z plane 18 side.

The inventor found that an absolute value of the tensile stress at aposition 78 that is apart from the neutral face 56 toward the +Z plane16 side at a distance L was higher than an absolute value of thecompressive stress at a position 80 that is apart from the neutral face56 toward the −Z plane 18 side at the distance L. That is, the inventorfound the tendency that the stress concentrated on the +Z plane 16 side.From this, the inventor considered that the rigidity with respect to thebending stress caused by the flexural vibration as the fundamental modeof the tuning fork type piezoelectric resonator element 10 at the +Zplane 16 side from the neutral face 56 was different from the rigidityat the −Z plane 18 side from the neutral face 56.

A variation of a natural resonance frequency of the fundamental mode ina case where acceleration in the Z-axis direction, that is, in thenormal line direction of the Z plane is applied to the tuning fork typepiezoelectric resonator element 10 was evaluated by a simulation and theresults are shown in FIG. 10B as frequency deviation. The frequencydeviation is a frequency variation, per unit change quantity, of theacceleration in the normal line direction of the Z plane. The unit usedin the embodiment is ppm/1 G. Here, the frequency variation per unitchange quantity of the acceleration in the Z-axis direction is sometimescalled thickness direction sensitivity.

Tuning fork type piezoelectric resonator elements used in thesimulations were a resonator element (1) having a shape with no grooveand made of an isotropic material; a resonator element (2) having ashape with no groove and made of an anisotropic material; a resonatorelement (3) having a groove formed at its +Z plane side and made of ananisotropic material; and a resonator element (4) having a groove formedat its −Z plane side and made of an anisotropic material.

The tuning fork type piezoelectric resonator elements (1) to (4) havethe shape shown in FIGS. 1A to 1C except for presence of the groove, andeach dimension thereof is defined as that shown in FIG. 10A. Here, theresonator element (3) having a groove formed at its +Z plane side andmade of an anisotropic material has a resonating arm of 1644 μm, butother examples (1), (2), and (4) have resonating arms that are fineadjusted. If dimensions of other parts are not changed, naturalresonance frequency Fd of the fundamental mode changes depending on thepresence of a groove, the position of the groove, and the material.However, the length of the resonating arm is fine adjusted so as not tochange dimensions of other parts and the natural resonance vibrationfrequency Fd. A natural resonance frequency of the fundamental wave modeof a cantilever is inversely proportional to the square of the length ofthe resonating arm in general.

As apparent from FIG. 10B, even in the examples having no groove, afrequency deviation of the example (2) made of the anisotropic materialis larger in about two digits than the example (1) made of the isotropicmaterial.

In a case of the examples made of the anisotropic material, a frequencydeviation of the example (3) having a groove formed on the +Z plane sidedecreased to be about a half of that of the example (2) having nogroove, while a frequency deviation of the example (4) having a grooveon the −Z plane side increased over that of the example (2).

From these results, it is considerable that if a groove is formed on the+Z plane side of the resonating arm, the rigidity with respect to thebending stress caused by the flexural vibration at the +Z plane side isdecreased so as to be balanced with the rigidity at the −Z plane side,accordingly decreasing the frequency deviation.

On the other hand, it is considerable that if a groove is formed on the−Z plane side of the resonating arm, the rigidity with respect to thebending stress caused by the flexural vibration at the −Z plane side isdecreased so as to make the difference from the rigidity at the +Z planeside larger and disrupt the balance, accordingly increasing thefrequency deviation,

Second Embodiment

FIG. 3A is a schematic view showing a tuning fork type piezoelectricresonator element 10 according to a second embodiment and FIG. 3B is asectional view showing an A-A line section of the resonator element 10.The tuning fork type piezoelectric resonator element 10 according to thesecond embodiment basically has the same configuration as that of thefirst embodiment. However, an adjusting part for adjusting the rigiditywith respect to flexural vibration of the resonating arm in theresonator element 10 in the second embodiment is a recess formed on the+Z plane from the base portion side along the free end direction of theresonating arm. Here, the tuning fork type piezoelectric resonatorelement in the second embodiment and that in embodiments described laterhave an excitation electrode film, but the structure of the excitationelectrode film is same as that in the first embodiment, so that thedescription thereof will be omitted.

In the second embodiment, a recess 58 can be formed by covering a tuningfork type piezoelectric resonator element plate (not shown) by a metalfilm in a manner leaving a portion on which a recess is to be formed andconducting an etching treatment. It is thinkable that the recess 58 isformed by widening the groove 26 of the first embodiment up to the samewidth as the width of the resonating arm 14 in the X-axis direction. Thebase portion 12 side of the resonating arm 14 is the portion thatreceives the strongest bending stress due to the flexural vibration, asdescribed above. If the recess 58 is formed on the portion, a portioncontributing most to the rigidity with respect to the flexural vibrationis cut out more than a case forming the groove 26. Accordingly, in acase where a recess and a groove formed from the base portion 12 sidealong the free end direction of the resonating arm 14 to have the samelengths are compared to each other, it is clear that the adjustingeffect of the recess with respect to the rigidity is larger than that ofthe groove. Conversely, the recess does not need to be formed to be longin the free end direction, and it is enough that the recess is formed ina small region including the base portion 12 side of the resonating arm14.

According to the second embodiment, if the recess 58 is formed on the +Zplane 16 of the resonating arm 14 in a manner positioned at the baseportion side, which is a portion receiving the strongest bending stressdue to the flexural vibration of the piezoelectric resonator element,the rigidity with respect to the bending stress caused by the flexuralvibration at the +Z plane 16 side can be effectively reduced only byetching a smaller region than the case of the first embodiment. Further,a high-accurate patterning in which positioning of the groove isconducted by photolithography is not required as a case described later,being able to increase a yield in manufacturing a piezoelectricresonator element.

Third Embodiment

FIG. 4 is a sectional view showing an A-A line section of a tuning forktype piezoelectric resonator element 10 according to a third embodiment.The tuning fork type piezoelectric resonator element 10 according to thethird embodiment has the same basic configuration as the firstembodiment. However, an adjusting part for adjusting the rigidity of theresonating arm of the resonator element 10 in the third embodimentincludes a first groove and a second groove. The first groove is formedon the +Z plane of the resonating arm from the base portion side alongthe free end direction, while the second groove is formed on the −Zplane of the resonating arm from the base portion side along the freeend direction of the arm. The first groove is formed to be deeper thanthe second groove. Forming the grooves on the both faces furtherdecreases the CI value of the tuning fork type piezoelectric resonatorelement 10 compared to the first embodiment. Here, the first groove andthe second groove have different depths. Therefore, a +Z plane groove 60that is the first groove and a −Z plane groove that is the second groovecan not be patterned and etched together, so that they need to be formedby separate processes. Further, the position of the +Z plane groove 60is same as that of the −Z plane groove 62 in the longitudinal directionof the resonating arm 14 when viewed from above, so that the sum of thedepths of the grooves can not be larger than the thickness of theresonating arm 14.

If the +Z plane groove 60 and the −Z plane groove 62 are formed on theresonating arm 14 as this, a portion contributing to the rigidity withrespect to the bending stress caused by the flexural vibration of theresonating arm 14 is removed, reducing the rigidity at the +Z plane 16side and that at the −Z plane 18 side. However, the +Z plane groove 60is formed deeper than the −Z plane groove 62, so that the rigidity atthe +Z plane 16 side is smaller by ratio so as to be a relatively closevalue to the rigidity at the −Z plane 18 side. Consequently, therigidity with respect to the bending stress caused by the flexuralvibration at the +Z plane 16 side is balanced with that at the FZ plane18 side.

According to the third embodiment, the grooves are formed on the rootportion 24, which receives the strongest bending stress due to theflexural vibration of the piezoelectric resonator element, of theresonating arm 14, that is, on the both faces at the base portion 12side so as to decrease the CI value of the tuning fork typepiezoelectric resonator element. Further, the +Z plane groove 60 isformed deeper than the −Z plane groove 62 so as to reduce a relativeintensity difference between the rigidity with respect to the bendingstress caused by the flexural vibration at the +Z plane 16 side and therigidity at the −Z plane 18 side. Thus the rigidity with respect to theflexural vibration at the +Z plane 16 side is balanced with the rigidityat the −Z plane 18 side so as to be able to reduce a component in theZ-axis direction of the flexural vibration of the resonating arm 14,that is, a component in the thickness direction. Accordingly, thepiezoelectric resonator element in which the detecting sensitivity ofthe acceleration in the thickness direction, that is, the sensitivity inother axis is reduced and have a low Cf value can be formed,

Fourth Embodiment

FIG. 5A is a schematic view showing a tuning fork type piezoelectricresonator element according to a fourth embodiment and FIG. 5B is asectional view showing a B-B line section. The tuning fork typepiezoelectric resonator element according to the fourth embodiment hasthe same basic configuration as that of the first embodiment. However,an adjusting part of the resonating arm in the resonator element of thefourth embodiment includes a first groove and a second groove. The firstgroove is formed on the +Z plane of the resonating arm from the baseportion side along the free end direction and the second groove isformed on the −Z plane of the resonating arm from the base portion sidealong the free end direction of the arm. An end at the base portion sideof the first groove is positioned closer to the base portion than an endat the base portion side of the second groove.

If a +Z plane groove 64 that is the first groove has a depth differentfrom that of a −Z plane groove 66 that is the second groove, the groovescan not be formed together by patterning in a photolithography processand etching. However, if they have the same depths, they can be formedat a time. Since the −Z plane groove 66 is formed from a basing pointthat is positioned more free end side than a terminating end of the +Zplane groove 64 along the free end side, so that the +Z plane groove 64and the −Z plane groove 66 do not interfere with each other, forming nopenetrating hole in the thickness direction of the resonating arm 14.Therefore, the grooves can be formed to have a depth that is close tothe thickness of the resonating arm 14. Accordingly, the CI value can bedecreased more than the case in the third embodiment.

The +Z plane groove 64 is formed at the base portion 12 side, which is aportion receiving the strongest bending stress due to the flexuralvibration, of the resonating arm 14, while the −Z plane groove 66 isformed on a position which receives small bending stress due to theflexural vibration and is quite apart from the base portion 12 of theresonating arm 14. Therefore, the +Z plane groove 64 have a largerreducing effect for the rigidity with respect to the bending stresscaused by the flexural vibration.

According to the fourth embodiment, the groove is formed on the +Z plane16 side of the resonating arm 14 in a manner positioned at the rootportion 24, that is, at the base portion 12 side, which is a portionreceiving the strongest bending stress due to the flexural vibration ofthe tuning fork type piezoelectric resonator element, so as toeffectively reduce the rigidity with respect to the bending stresscaused by the flexural vibration. Thus the rigidity with respect to thebending stress caused by the flexural vibration at the +Z plane 16 sidecan be balanced with that at the −Z plane 18 side. Further, the +Z planegroove 64 and the −Z plane groove 66 do not interfere with each other inthe thickness direction. Therefore, the design versatility in the depthdirection of the groove is improved more than that of the thirdembodiment. At the same time, since the groove can be designed deeperthan that in the third embodiment, the piezoelectric resonator elementthat has a smaller CI value than that in the third embodiment can beformed. Further, asymmetry property in the thickness direction isimproved compared to the third embodiment, being able to improvesuppressing effect of an occurrence of unnecessary vibration caused bythe thickness dimension.

Furthermore, as shown in FIG. 5C, an overlapping region 67 on which thefirst groove and the second groove are overlapped when they are viewedfrom the thickness direction may be formed at the end at the baseportion 12 side of the −Z plane groove 66. On the overlapping region 67,the end at the base portion 12 side of the −Z plane groove 66 that isthe second groove is positioned closer to the base portion 12 than theend at the free end side of the +Z plane groove 64 that is the firstgroove. The overlapping region 67 can be formed depending on thedifference between etching velocities of crystal faces. The differenceis caused by anisotropy of crystal. Therefore, if the anisotropy etchingis used, the +Z plane groove 64 and the −Z plane groove 66 can be formedwhile forming the overlapping region 67 without penetration.

In the structure shown in FIG. 5C, the +Z plane groove 64 that is formedat the +Z plane 16 side and the −Z plane groove 66 that is formed at the−Z plane 18 side do not interfere with each other in the depthdirection, improving the design versatility of the grooves in the depthdirection. Further, the resonating arm 14 becomes thin in the thicknessdirection and the distance between the excitation electrodes formed inthe grooves of the both faces becomes short in the overlapping region67, being able to apply large electrical field to the overlapping region67. Therefore, the piezoelectric resonator element having furtherreduced CI value can be formed. Further, a groove region contacts withan etchant more sparsely than an outer shape region, so that the etchingvelocity in the groove region is slower than that in the outer shaperegion. Therefore, no particular process for digging the groove isrequired and the groove can be formed at the same time with the outershape blanking of the piezoelectric resonator element, being able toform the piezoelectric resonator element having a higher yield than thecases described above.

Fifth Embodiment

FIG. 6A is a sectional view showing a B-B line section of a tuning forktype piezoelectric resonator element according to a fifth embodiment.The tuning fork type piezoelectric resonator element 10 according to thefifth embodiment basically has the same configuration as that of thefirst embodiment as shown in FIG. 6A. However, an adjusting part of theresonating arm in the resonator element of the fifth embodiment includesa first groove, a second groove, and a beam. The first groove is formedon the +Z plane from the base portion side of the resonating arm alongthe free end direction. The second groove is formed on the −Z plane fromthe base portion side of the resonating arm along the free enddirection. The beam is formed at the base portion side of the secondgroove and is positioned apart from the base portion side of the secondgroove to the free end side.

Since a +Z plane groove 68 that is the first groove and a −Z planegroove 70 that is the second groove have the same depths, they can beformed together by patterning and etching together with a beam 72. Sincethe depths and positions in the longitudinal direction of the grooves atthe +Z plane 16 side and at the −Z plane 18 side are same, therigidities with respect to the flexural vibration are decreased in thesame proportion when only the grooves are considered. However, the beam72 is formed in the −Z plane groove 70 on the root portion 24, that is,at the base portion 12 side so as to contribute to the increase of therigidity with respect to the bending stress caused by the flexuralvibration. Consequently, the rigidity at the −Z plane 18 side isincreased relatively to that at the +Z plane 16 side, being able tostrike the balance between the rigidity at the +Z plane 16 side and thatat the −Z plane 18 side.

In addition, the position of the beam 72 can be arbitrarily determinedin the −Z plane groove 70 in patterning, as shown in FIG. 6B. Since theroot portion 24 of the resonating arm 14, that is, at the base portion12 side of the arm 14 is a portion that receives the strongest bendingstress due to the flexural vibration as described above, the rigiditywith respect to the bending stress caused by the flexural vibration isincreased most in a case where the beam 72 is formed on the base portion12 side. If the beam 72 is formed on the free end side of the arm, therigidity at the −Z plane 18 side is most decreased, but the rigidity atthe −Z plane 18 side is adjusted to be larger than a case where the beam72 is not formed in the −Z plane groove 70. Namely, changing theposition of the beam 72 can control the rigidity at the −Z plane 18 sideso as to strike the balance between the rigidity with respect to thebending stress caused by the flexural vibration at the +Z plane 16 sideand that at the −Z plane 18 side.

According to the fifth embodiment, the −Z plane groove 70 can be formedto be shorter than the +Z plane groove 68 in order to make the baseportion 12 side, which is a portion receiving the strongest bendingstress due to the flexural vibration of the piezoelectric resonatorelement, of the resonating arm 14 thick. Therefore, even if the beam 72is formed to be short, the rigidity with respect to the bending stresscaused by the flexural vibration at the −Z plane 18 side is relativelyincreased so as to strike the balance between the rigidity of theresonating arm 14 at the +Z plane 16 side and that at the −Z plane 18side. Further, since the length of the groove to which the excitationelectrode film is formed can be sufficiently secured, electrodes of thepiezoelectric resonator can be widely formed in the groove. Since thegrooves are formed on the both faces, the piezoelectric resonatorelement having an IC value that is not inferior to that in the thirdembodiment can be formed. Further, forming the beam 72 improves theasymmetry property in the thickness direction compared to the thirdembodiment, improving the suppressing effect of the occurrence of theunnecessary vibration depending on the thickness dimension. Furthermore,the more the beam 72 is apart from the base portion 12 side to the freeend side in the −Z plane groove 70, the more the rigidity with respectto the bending stress caused by the flexural vibration of the −Z plane18 can be decreased. Therefore, proper determination of the position ofthe beam 72 can fine-adjust the rigidity with respect to the bendingstress caused by the flexural vibration at the −Z plane 18 of theresonating arm 14. In addition, if the position of the beam 72 isproperly determined, the degree of the asymmetry in the thicknessdirection can be determined, being able to optimize for controlling theunnecessary vibration.

Sixth Embodiment

FIG. 7A is a sectional view showing a B-B line section of a tuning forktype piezoelectric resonator element 10 according to a sixth embodiment.The tuning fork type piezoelectric resonator element according to thesixth embodiment basically has the same configuration as that of thefirst embodiment. However, the adjusting part for adjusting the rigidityincludes a first electrode film that is formed on the +Z plane of theresonating arm, and a second electrode film that is formed on the −Zplane of the resonating arm and is thicker than the first electrodefilm.

In the sixth embodiment, the balance between the rigidity with respectto the bending stress caused by the flexural vibration at the +Z plane16 side and that at the −Z plane 18 side is adjusted by electrode films74. The electrode film 74 is composed of a first excitation electrodefilm 46, a second excitation electrode film 48, and a third excitationelectrode film 50 that vibrate the resonating arm 14 of the tuning forktype piezoelectric resonator element 10, an extraction electrode film52, and a connecting electrode film 54. The electrode film 74 formed onthe +Z plane 16 side of the resonating arm 14 is thinner than theelectrode film 74 formed on the −Z plane 18 side so as to relativelyincrease the rigidity with respect to the bending stress caused by theflexural vibration at the −Z plane 18 side. Therefore, the neutral face56 is shifted to the central region in the thickness direction so as tostrike the balance between the rigidities with respect to the flexuralvibration of the resonating arm 14 The electrode film 74 is made of Cr,Au, Al, and the like as described above. An electrode pattern of theelectrode film 74 composed of the first excitation electrode film 46,the second excitation electrode film 48, the third excitation electrodefilm 50, the extraction electrode film 52, and the connecting electrodefilm 54 is same as that in the first embodiment.

In a case where the rigidity with respect to the bending stress causedby the flexural vibration of the resonating arm 14 is adjusted by usingthe electrode film 74, Young's moduli of quarts crystal and these metalsare important. As Young's modulus increases, deformation with respect totension and compression decreases, increasing the rigidity.

In this embodiment, Young's modulus (285 GPa) of Cr is higher thanYoung's modulus (82 GPa) of Au and that (69 GPa) of Al. On the otherhand, Young's modulus of quartz crystal is about 100 GPa on the Z plane.Thus Young's modulus of Cr is higher than that of quartz crystal, sothat an adjusting effect obtained by forming the electrode film 74 b onthe FZ plane 18 relatively thicker than the electrode film 74 a on the+Z plane 16 is large in a case where the electrode films 74 are made ofCr.

The electrode films 74 are formed by spattering and the like. If thetime for spattering the −Z plane 18 side is made longer than that forspattering the +Z plane 16 side, for example, the electrode film 74 onthe −Z plane 18 can be formed thicker than that on the +Z plane 16.Thus, adjusting the material and the thickness of the electrode film 74can adjust the balance between the rigidity with respect to the bendingstress caused by the flexural vibration on the +Z plane 16 and that onthe −Z plane 18. Further, as shown in the B-B line sectional view ofFIG. 7B, even after grooves and the like are formed on the tuning forktype piezoelectric resonator element 10 like the first to fifthembodiments (FIG. 7B shows a case using the fifth embodiment), theelectrode films 74 can be formed with no limitation.

According to the sixth embodiment, the electrode film on the −Z plane 13is formed thicker than that on the +Z plane 16 without conducting aspecific etching treatment for forming the grooves and the likedescribed above on the piezoelectric resonator element. This relativelyincreases the rigidity with respect to the bending stress caused by theflexural vibration at the −Z plane 18 side. Accordingly, the rigiditiesof the both faces with respect to the bending stress caused by theflexural vibration are balanced, being able to decrease a component ofthe flexural vibration in the Z-axis direction of the resonating arm 14.Therefore, the piezoelectric resonator element in which the detectingsensitivity of the acceleration in the Z-axis direction, that is, thethickness direction, that is, the sensitivity in other axis is reducedcan be formed. Further, since the piezoelectric resonator elementrequires no grooves, for example, formed thereon, a manufacturingprocess does not become complex, being able to increase a yield ofmanufacturing the piezoelectric resonator element. In addition, if thepresent embodiment is applied to the piezoelectric resonator element ofthe first to fifth embodiments, not only the grooves and the like formedby etching but also the electrode films 74 adjust the balance betweenthe rigidity with respect to the bending stress caused by the flexuralvibration on the +Z plane 16 and that on the −Z plane 18. Therefore, theadjusting range of the rigidities on the +Z plane 16 and the −Z plane 18is increased, being able to more effectively decrease the sensitivity inother axis.

Seventh Embodiment

FIG. 8 is a schematic view showing a piezoelectric resonator and anacceleration sensor according to a seventh embodiment. The piezoelectricresonator and the acceleration sensor according to the seventhembodiment are provided with the tuning fork type piezoelectricresonator element 10 of any of the first to sixth embodiments. Theresonator element 10 is mounted such that the base portion 12 thereof issupported in a cantilever state. An acceleration sensor 82 of theseventh embodiment is formed such that an external circuit which is notshown is wired to a piezoelectric resonator composed of thepiezoelectric resonator element 10, a mount electrode 84, a package 86,and a lid 88 made of thin plate glass and the like. The tuning fork typepiezoelectric resonator element 10 is fixed in a cantilever-supportedstate that the base portion 12 as a fixing end is bonded through themounting electrode 84 to a bottom face of the package 86. The lid 88 isbonded to the upper surface of the package 86 by seam welding, after thetuning fork type piezoelectric resonator element 10 is mounted on thepackage 86. With such structure, the acceleration sensor 82 that reducesthe sensitivity in other axis such as the Z-axis direction, that is, thethickness direction and uses the Y-axis direction as the accelerationdetecting axis can be formed.

The acceleration sensor 82 requires fine adjustment of a vibratingfrequency after mounting. The fine adjustment of the vibrating frequencycan be conducted such that a portion, which is positioned on theconnecting electrode film 54 formed at the free end side of theresonating arm, of the electrode film 74 is removed by laser 90 so as tochange a mass of the arm. However, even though a mass at the baseportion 12 side is changed, the vibrating frequency hardly changes. Onthe other hand, the rigidities on the +Z plane 16 and on the −Z plane 18can be adjusted by removing a portion, which covers the base portion 12side of the resonating arm 14, of the electrode films 74 by the laser90. The variation of the rigidity with respect to the bending stresscaused by the flexural vibration on the +Z plane 16 and on the −Z plane18 is most affected by the change of the mass at the base portion 12side of the resonating arm 14. Therefore, even if the mass at theconnecting electrode film 54 side is changed by the laser 90, thebalance of the rigidities of the piezoelectric resonator element 10 ishardly affected. Accordingly, if the tuning fork type piezoelectricresonator element 10 of the sixth embodiment is mounted with the lid 88made of a material through which the laser 90 is transmitted (thin plateglass, for example) as shown in FIG. 8, the resonance frequency can befine-adjusted by irradiation of the laser 90 and the balance between therigidities with respect to the bending stress caused by the flexuralvibration can be adjusted by the irradiation of the laser 90 even afterthe mounting. At this time, any face of the +Z plane 16 and the −Z plane18 may be used as a bonding face with respect to the mount electrode 84.Of course, the rigidity of the face from which the electrode film 74 isremoved by the irradiation of the laser 90 is decreased.

According to the seventh embodiment, the acceleration sensor includingthe piezoelectric resonator element that uses the longitudinal directionas the acceleration detecting axis and reduces the sensitivity in otheraxis by reducing a vibrating component in the Z-axis direction of theflexural vibration can be formed. Further, the frequency adjustmentafter the mounting is conducted at the free end side of the resonatingarm, while the rigidity adjustment is conducted at the base portion sideof the resonating arm. Therefore, the frequency adjustment and therigidity adjustment do not interfere with each other so as to beconducted independently.

The tuning fork type piezoelectric resonator element having tworesonating arms that are cantilever-supported has been mentioned in theabove embodiments, but it should be noted that the embodiments areapplicable to even a resonator element having one resonating arm or aresonator element having two or more resonating arms. Further, thepiezoelectric resonator element is applicable not only to theacceleration sensor but also other piezoelectric devices such as a clocksource.

The piezoelectric resonator element of any of the embodiments includes:the resonating arm extending in a first direction andcantilever-supported; the base portion cantilever-supporting theresonating arm; and the excitation electrode allowing the resonating armto perform flexural vibration in a second direction that is orthogonalto the first direction. In the resonator element, the resonating armincludes the adjusting part for the rigidity with respect to a bend in athird direction that is orthogonal to the first and second directions.

In the piezoelectric resonator element composed of a piezoelectricplate, rigidities with respect to a bending stress and the like on facesare sometimes different from each other due to the anisotropy of theplate. If such piezoelectric resonator element is allowed to performflexural vibration by the excitation electrode, the vibration includesnot only a component in a predetermined vibrating direction but also acomponent of vibration in a direction that is orthogonal to thepredetermined vibrating direction. Therefore, according to theembodiments of the invention, balancing the rigidities with respect tothe flexural vibration can reduce a component of vibration in adirection orthogonal to that of the flexural vibration of the resonatingarm. Accordingly, the piezoelectric resonator element that reduces theoccurrence of deviation, which is caused by the acceleration from thethird direction, of the resonance frequency of the flexural vibrationcan be formed.

Therefore, the piezoelectric resonator element that performs theflexural vibration in a direction (the second direction, X direction)orthogonal to the longitudinal direction (the first direction, Ydirection) and decreases the sensitivity in other axis by decreasing avibrating component in the Z direction of the flexural vibration can beformed, and the piezoelectric resonator and the piezoelectric deviceincluding the piezoelectric resonator element supported at its baseportion as a fixed end in a cantilever state can be formed.

The entire disclosure of Japanese Patent Application No. 2007-285890,filed Nov. 2, 2007 is expressly incorporated by reference herein.

1. A piezoelectric resonator element, comprising: a resonating armcomposed of a Z-cut piezoelectric plate and cantilever-supported in alongitudinal direction; a base portion cantilever-supporting theresonating arm; and an excitation electrode exciting the resonating armto perform flexural vibration in a direction orthogonal to a thicknessdirection, wherein the resonating arm includes an adjusting partadjusting rigidity with respect to a bend in the thickness direction,wherein the adjusting part includes a first groove formed from the baseportion side of the +Z plane of the resonating arm along the free enddirection of the resonating arm and a second groove formed from the baseportion side of a −Z plane of the resonating arm along the free enddirection of the resonating arm, and the first groove is formed deeperthan the second groove.
 2. The piezoelectric resonator element accordingto claim 1, wherein the adjusting part includes a first electrode filmformed on the +Z plane of the resonating arm and a second electrode filmformed on the −Z plane of the resonating arm and being thinner than thefirst electrode film.
 3. The piezoelectric resonator element accordingto claim 1, wherein the resonating arm includes two resonating arms, theexcitation electrode includes a plurality of excitation electrodes, thetwo resonating arms are cantilever-supported at the base portion inparallel, and an excitation electrode formed on one resonating arm andanother excitation electrode formed on the other resonating arm arecoupled by cross wiring.
 4. A piezoelectric resonator, comprising thepiezoelectric resonator element according to claim 1, the piezoelectricresonator element being mounted in a cantilever-supported state in whichthe base portion of the resonator element is used as a fixed end.
 5. Apiezoelectric resonator element, comprising: a resonating arm composedof a Z-cut piezoelectric plate and cantilever-supported in alongitudinal direction: a base portion cantilever-supporting theresonating arm: and an excitation electrode exciting the resonating armto perform flexural vibration in a direction orthogonal to a thicknessdirection, wherein the resonating arm includes an adjusting partadjusting rigidity with respect to a bend in the thickness direction,wherein the adjusting part includes a first groove formed from the baseportion side of the +Z plane of the resonating arm along the free enddirection of the resonating arm and a second groove formed from the baseportion side of the −Z plane of the resonating arm along the free enddirection of the resonating arm, and an end at the base portion side ofthe first groove is positioned closer to the base portion than an end atthe base portion side of the second groove; and an overlapping region inwhich the end at the base portion side of the second groove ispositioned closer to the base portion than the end at a free end side ofthe first groove and the first groove and the second groove areoverlapped with each other when they are viewed from the thicknessdirection is formed at the end at the base portion side of the secondgroove.
 6. The piezoelectric resonator element according to claim 5,wherein the adjusting part includes a first electrode film formed on the+Z plane of the resonating arm and a second electrode film formed on the−Z plane of the resonating arm and being thinner than the firstelectrode film.
 7. The piezoelectric resonator element according toclaim 5, wherein the resonating arm includes two resonating arms, theexcitation electrode includes a plurality of excitation electrodes, thetwo resonating arms are cantilever-supported at the base portion inparallel, and an excitation electrode formed on one resonating arm andanother excitation electrode formed on the other resonating arm arecoupled by cross wiring.
 8. A piezoelectric resonator, comprising thepiezoelectric resonator element according to claim 5, the piezoelectricresonator element being mounted in a cantilever-supported state in whichthe base portion of the resonator element is used as a fixed end.